Online Optimization Research Articles

Distributed Drive Electric Vehicle Handling Stability Coordination Control Framework Based on Adaptive Model Predictive Control.

Distributed drive electric vehicles improve steering response and enhance overall vehicle stability by independently controlling each motor. This paper introduces a control framework based on Adaptive Model Predictive Control (AMPC) for coordinating handling stability, consisting of three layers: the dynamic supervision layer, online optimization layer, and low-level control layer. The dynamic supervision layer considers the yaw rate and maneuverability limits when establishing the β-β˙ phase plane stability boundary and designs variable weight factors based on this stability boundary. The online optimization layer constructs the target weight-adaptive AMPC strategy, which can adjust the control weights for maneuverability and lateral stability in real time based on the variable weight factors provided by the dynamic supervision layer. The low-level control layer precisely allocates the driver's requested driving force and additional yaw moment by using torque distribution error and tire utilization as the cost function. Finally, experiments are conducted on a Simulink-CarSim co-simulation platform to assess the performance of AMPC. Simulation results show that, compared to the traditional MPC strategy, this control strategy not only enhances maneuverability under normal conditions but also improves lateral stability control under extreme conditions.

Data-driven thermal modeling of in-situ Automated Fiber Placement

This study proposes a data-driven model for thermal history prediction during in-situ Automated Fiber Placement of thermoplastic composites. Temperature data was experimentally collected with fast-response thermocouples placed within carbon fiber AS4/PEEK composite substrates. The temperature for various combinations of hot gas torch temperatures, heat source velocity, and locations through the thickness and width were collected. A feedforward neural network (FNN) was developed to predict the entire 3-dimensional thermal history. The FNN had five input features and one output: the temperature at a given position and a combination of the process parameters. The FNN predictions for data unseen during training are validated for cases of interpolation and extrapolation. As expected, suitable performance was obtained for cases of interpolation, but predictions suffered in extrapolation. The computational efficiency of FNNs makes them an appropriate candidate for on-line thermal history prediction or process optimization, given that they are used within their training range.

Entry guidance for spatial no-fly zones avoidance via model-based reinforcement learning

This paper proposes a novel guidance law for hypersonic entry vehicles, considering no-fly zones with height limits. Traditional planar assumptions restrict the flexibility of trajectory design for scenarios like radar avoidance. Besides, the numerical integration proves inefficient for long-term prediction and avoidance. Therefore, a model-based reinforcement learning policy is designed. It offline learns entry dynamics in advance and onboard plans a feasible trajectory. The planner's state includes flight status and no-fly zones; action presents waypoints; and reward ensures constraint while maximizing terminal precision. Then, analytical prediction converts spatial no-fly zone constraints to flight-path angle constraints, improving precision compared to traditional one-step estimates. Finally, the two parts are assembled into the predictor-corrector framework, which gives the augmented guidance commands. While retaining its robustness to bias, our method reduces online optimization calculations and outperforms constraint satisfaction. Experiments show that the model-based method reduces 60% training in offline training compared with proximal policy optimization. Besides, our method is 80% faster than conventional predictor-corrector guidance regarding online computation speed.

Distributed online optimization for integrated energy systems: A multi‐agent system consensus approach

SummaryThe integration of multi‐energy within distribution networks has escalated the need for efficient operation and control of integrated energy systems (IES). Addressing the complexities of real‐time scheduling and low‐carbon optimization, we propose a novel artificial intelligence driven multi‐agent system (MAS) approach for modeling the interactions and operations within the multi‐agent integrated energy systems (MA‐IES) framework. In this framework, distinct components such as electric, gas, and heat networks are conceptualized as autonomous agents, each responsible for managing its domain while interacting with other agents to achieve system‐wide efficiency and economical goals. The agents communicate and coordinate through a distributed online optimization framework, utilizing the alternating direction multiplier method (ADMM) to ensure effective consensus despite the inherent nontransparency of information exchange. This MAS based approach allows for dynamic adaptation of strategies based on local data and global objectives, significantly enhancing the responsiveness and adaptability of MA‐IES. We further integrate an objective function reliant on a tiered carbon pricing mechanism to assess and minimize the environmental impact of operations. Enhanced by adaptive penalty coefficients within the ADMM, our MA‐IES framework demonstrates improved convergence rates and robustness in operational scenarios. Empirical validation through detailed case studies confirms the superior performance of our MAS‐based model, demonstrating its potential to realize an efficient and economical low‐carbon operation of MA‐IES.

Accelerated MPC: A real-time model predictive control acceleration method based on TSMixer and 2D block stochastic configuration network imitative controller

Modern industrial processes demand real-time model predictive control (MPC) method within the constraints of limited computing resources. This paper introduces an accelerated MPC method to address the issue. Specifically, we employ the time series mixing model (TSMixer) to construct a predictive model capable of accurately forecasting the behavior of the system under control. Furthermore, we extend the capabilities of TSMixer by integrating a feature classification model (TSMixer with FCM). This enhanced version takes into account both future information and static variables, resulting in superior accuracy compared to the transformer model while maintaining a significantly smaller parameter count. Finally, to further enhance MPC’s responsiveness, we develop a two-dimensional block stochastic configuration network (2D-BSCN) imitative controller. This innovative network clones the behavior of rolling optimization, effectively replacing online optimization to reduce computational time. The experimental results show that the accelerated MPC has an excellent performance in numerical simulation and actual industrial processes. Notably, the algorithm achieves a smaller FLOPs and tracking time than other state-of-the-art models, well within the requirement for industrial process control.

Technical Note—Near-Optimal Bayesian Online Assortment of Reusable Resources

Near-Optimal Bayesian Online Assortment of Reusable Resources Motivated by rental services in e-commerce, we consider revenue maximization in the online assortment of reusable resources for different types of arriving consumers. We design competitive online algorithms compared with the optimal online policy in the Bayesian setting, where consumer types are drawn independently from known heterogeneous distributions over time. In scenarios with large initial inventories, our main result is a near-optimal competitive algorithm for reusable resources. Our algorithm relies on an expected linear programming (LP) benchmark, solves this LP, and simulates the solution through independent randomized rounding. The main challenge is achieving inventory feasibility efficiently using these simulation-based algorithms. To address this, we design discarding policies for each resource, balancing inventory feasibility and revenue loss. Discarding a unit of a resource impacts future consumption of other resources, so we introduce postprocessing assortment procedures to design and analyze our discarding policies. Additionally, we present an improved competitive algorithm for nonreusable resources and evaluate our algorithms using numerical simulations on synthetic data.

Lyapunov-based model predictive control for trajectory tracking of hovercraft with actuator constraints and external disturbances

In this study, a Lyapunov-based model predictive control (LMPC) method is developed to address the trajectory tracking problem of autonomous hovercrafts subjected to unknown complex disturbances from ocean environments and practical constraints of marine surface vessels, such as actuator increment limitations and saturation. Initially, the novel LMPC algorithm is applied to enhance tracking performance through rolling optimization and online optimization. Subsequently, a nonlinear disturbance observer is designed to estimate external disturbances caused by wind and dynamics uncertainties. Furthermore, to theoretically ensure control stability, contraction constraints are established using the nonlinear backstepping control method. This approach provides the essential conditions for the system's robustness and stability. Finally, the superiority and robustness of the designed LMPC trajectory tracking method are demonstrated through numerical simulations conducted in a marine environment.

Physics-Informed Online Learning for Temperature Prediction in Metal AM.

In metal additive manufacturing (AM), precise temperature field prediction is crucial for process monitoring, automation, control, and optimization. Traditional methods, primarily offline and data-driven, struggle with adapting to real-time changes and new process scenarios, which limits their applicability for effective AM process control. To address these challenges, this paper introduces the first physics-informed (PI) online learning framework specifically designed for temperature prediction in metal AM. Utilizing a physics-informed neural network (PINN), this framework integrates a neural network architecture with physics-informed inputs and loss functions. Pretrained on a known process to establish a baseline, the PINN transitions to an online learning phase, dynamically updating its weights in response to new, unseen data. This adaptation allows the model to continuously refine its predictions in real-time. By integrating physics-informed components, the PINN leverages prior knowledge about the manufacturing processes, enabling rapid adjustments to process parameters, geometries, deposition patterns, and materials. Empirical results confirm the robust performance of this PI online learning framework in accurately predicting temperature fields for unseen processes across various conditions. It notably surpasses traditional data-driven models, especially in critical areas like the Heat Affected Zone (HAZ) and melt pool. The PINN's use of physical laws and prior knowledge not only provides a significant advantage over conventional models but also ensures more accurate predictions under diverse conditions. Furthermore, our analysis of key hyperparameters-the learning rate and batch size of the online learning phase-highlights their roles in optimizing the learning process and enhancing the framework's overall effectiveness. This approach demonstrates significant potential to improve the online control and optimization of metal AM processes.

Distributed Online Optimization Under Dynamic Adaptive Quantization

Distributed Online Optimization Under Dynamic Adaptive Quantization

Online optimal scheduling for battery swapping charging systems with partial delivery

Battery swapping–charging system (BSCS) is a promising operating paradigm to provide centering charging and battery swapping service for electric vehicles in transportation electrification. Facing real-time information on battery demand under the limited transporting trucks, flexible online optimization of battery delivery and transportation routing is essential for meeting practical requirements. This paper investigates the real-time scheduling problem in BSCS, considering the battery partial delivery, energy demand, delivery deadline, and vehicle routing. Considering the non-deterministic polynomia hardness of battery transportation, the offline BSCS is a time-consuming task and is unsuitable for the online setting. A Lagrangian relaxation-based Benders decomposition is proposed for parallel and real-time implementation, improving the scheduling efficiency. To tackle future information such as battery demands and delivery deadlines, by introducing the dummy copy, the offline algorithm is embedded within a rolling horizon framework to solve in real-time repeatedly. Finally, case studies using real road maps in Shanghai and Belgium have verified the validity of the proposed online framework and confirmed the necessity of considering partial delivery in enhancing the operation flexibility of BSCS. The computational efficiency of the proposed algorithm is studied under different scales of the road network, and the profit from partial delivery and online implementation are highlighted.

Distributed sequential optimal power flow under uncertainty in power distribution systems: A data-driven approach

Modern distribution systems with high penetration of distributed energy resources face multiple sources of uncertainty. This transforms the traditional Optimal Power Flow problem into a problem of sequential decision-making under uncertainty. In this framework, the solution concept takes the form of a policy, i.e., a method of making dispatch decisions when presented with a real-time system state. Reasoning over the future uncertainty realization and the optimal online dispatch decisions is especially challenging when the number of resources increases and only a small dataset is available for the system’s random variables. In this paper, we present a data-driven distributed policy for making dispatch decisions online and under uncertainty. The policy is assisted by a Graph Neural Network but is constructed in such a way that the resulting dispatch is guaranteed to satisfy the system’s constraints. The proposed policy is experimentally shown to achieve a performance close to the optimal-in-hindsight solution, significantly outperforming state-of-the-art policies based on stochastic programming and plain machine-learning approaches.

Tuning and testing an Online Feedback Optimization controller to provide curative distribution grid flexibility

Due to more volatile generation, flexibility will become more important in transmission grids. One potential source of this flexibility can be distribution grids. A flexibility request from the transmission grid to a distribution grid then needs to be split up onto the different Flexibility Providing Units (FPU)s in the distribution grid. One potential way to do this is Online Feedback Optimization (OFO). OFO is a new control method that steers power systems to the optimal solution of an optimization problem using minimal model information and computation power. This paper will show how to choose the optimization problem and how to tune the OFO controller. Afterward, we test the resulting controller on a real distribution grid laboratory and show its performance, its interaction with other controllers in the grid, and how it copes with disturbances. Overall, the paper makes a clear recommendation on how to phrase the optimization problem and tune the OFO controller. Furthermore, it experimentally verifies that an OFO controller is a powerful tool to disaggregate flexibility requests onto FPUs while satisfying operational constraints inside the flexibility providing distribution grid.

Safe online optimization of motor speed synchronization control with incremental Q-learning

Reinforcement learning (RL) is promising for online controller optimization. However, its practical application has been hindered by safety issues. This paper proposes an algorithm named Incremental Q-learning (IQ) and applies it to the online optimization of motor speed synchronization control. IQ ensures safe learning by adopting so-called incremental action variables which represent incremental change rather than absolute magnitude, and dividing the one-round learning process in the classic Q-learning (in this paper referred to as Absolute Q-learning, AQ) into multiple consecutive ones with the Q table getting reset at the beginning of each round. Since the permitted interval of change is restricted to be very small, the agent can learn its way safely, steadily, and robustly towards the optimal policy. Simulation results show that IQ is advantageous to AQ in optimality, safety, and adaptability. IQ converges to better final performances with significantly smaller performance variance along the whole learning process, smaller torque trajectory deviation between consecutive episodes and adapts to unknown disturbances faster. It is of great potential for online controller optimization/tuning in practical engineering projects. Source code and demos are provided.

Distributed model predictive control of fan coil system

To address the issues of large overshoot, long system stabilization time, and slow response associated with traditional PID-based and centralized model predictive control (MPC) of fan coil systems, this study proposes a distributed model predictive control (DMPC) method suitable for multi-zone building temperature regulation. Specifically, based on the thermal dynamic model of different zones, and aiming to constrain indoor temperature within set limits and minimize water system pressure drop and fan coil speed, a distributed MPC architecture for fan coil systems is developed. To solve the distributed optimization problem, the Nash equilibrium is introduced to find the global balance point within the distributed structure, and the Beetle Antennae Search-Particle Swarm Optimization (BAS-PSO) hybrid algorithm is used for online optimization of local MPCs. Experimental results show that compared to traditional PID control, the distributed MPC achieves coordinated multi-zone indoor temperature regulation with better dynamic performance, with the average absolute temperature error in each zone below 5 % and an energy savings rate of 16.23 %. Through semi-physical simulation, it is demonstrated that the proposed distributed MPC method has better applicability when the number of fan coils exceeds 10, compared to centralized MPC.

Online optimization of petrochemical process via case-based reasoning and conditional mutual information

The strict mechanism model of petrochemical processes is often complex, resulting in long modeling times, low computational efficiency, and poor accuracy, which limits the application of mechanistic models in process optimization and advanced control. The advent of big data technology provides new solutions for this problem. Herein, a new method based on historical Case-Based Reasoning (CBR) is proposed to process online optimization and calculate variable attribute weights for case retrieval using conditional mutual information. Considering the process time-lag characteristics, a piecewise sequential CBR method for optimization is further proposed, which directly recognizes the pattern based on the industrial past data and amply utilized the process information. For case study and method validation, the approach is applied to an actual fluid catalytic cracking (FCC) process, converting low-quality heavy oils into valuable light transportation fuels and chemicals such as gasoline and propylene. As demonstrated by the case study results, the proposed method increases the average yield of gasoline and total liquid respectively by 2.5 % and 4.0 % while decreasing the average yield of coke by 1.3 %. The results further indicate that the overall optimization performance is comparable to many advanced intellectual optimization algorithms, allowing favorable operability and ensuring good robustness for different optimization targets. It could provide a solution with high accuracy and good adaptability for online process optimization in complex chemical processes.

Divertor-safe nonlinear burn control based on a SOLPS parameterized core-edge model for ITER

For ITER operations, the range of desirable burning-plasma regimes with high fusion power output will be restricted by various operational constraints. These constraints include the saturation of ITER’s various heating and fueling actuators such as the neutral beam injectors, the ion and electron cyclotron heating systems, the gas puffing system, and the deuterium–tritium pellet injectors. In addition to these actuator constraints, the H-mode power threshold, divertor detachment, and the heat load on the divertor targets may apply limitations to ITER’s operational space. In this work, Plasma Operation Contour (POPCON) plots that map the aforementioned constraints to the temperature-density space are used to investigate which constraints are most limiting towards accessing regimes with high fusion power output. The presented POPCON plots are based on a control-oriented core-edge model that couples the nonlinear density and energy response models for the core-plasma region with SOLPS4.3 parameterizations for conditions in the edge-plasma regions (scrape-off-layer and divertor). Using this control-oriented core-edge model, a nonlinear burn controller, which aims to regulate the plasma temperature and density in the core-plasma region, is constructed in this work. This controller is augmented with an online optimization scheme that governs the control references such that the plasma can be guided towards regimes with high fusion powers while protecting the divertor targets from dangerously high heat loads. A closed-loop simulation study illustrates the capability of this burn control scheme.

Best practices in online/distance pharmacy practice course didactic instruction

AbstractThis commentary provides an overview of the current literature and best practices for online learning and assessment within the didactic curriculum of pharmacy education, building on the 2022 ACCP commentary addressing remote experiential learning. Lessons learned from online delivery of curricula and best practices for programs to create the optimal online learning environment for students are reviewed. Although benefits of online learning have been found, such as flexibility, convenience, and efficient use of time, with similar short‐term student performance, the potential long‐term implications on pharmacy students are not fully known, particularly concerning board pass rates, job attainment, and knowledge/skills application in the workplace. This commentary reviews and recommends the types of teaching modalities that align best with an online format for knowledge acquisition and student satisfaction. The most challenging part of didactic curricula to teach remotely is skills development. Proficiency in skills (e.g., compounding preparations or physical assessment) is best evaluated in person to promote student self‐confidence in pharmacy practice and patient care. This commentary reviews the needed components for designing quality online courses, all in the context of remembering the significance of instructor engagement. The commentary also discusses the importance of bidirectional feedback for the instructor and student and the deliberate use of formative assessments of learning to gauge student performance. A review of online summative and high‐stakes assessments is included with a focus on ensuring academic integrity while also minimizing any impact on student performance and anxiety. As pharmacy education has learned from the experiences with the COVID‐19 transition to online learning, consideration should be given to best practices regarding when and how to use online modalities to teach students and foster student learning. Regardless of the format, courses should engage the student and instructor and be evaluated routinely to promote achievement of learning outcomes.

Optimization of air distribution and coal blending in pulverized coal boilers for high-temperature corrosion prevention based on POD reduced-order modeling

High-temperature corrosion in coal-fired boilers poses a significant threat to safe operation. However, there is currently a lack of effective online monitoring and optimization methods for high-temperature corrosion. Therefore, this study proposes a novel approach to rapidly predict the distribution of chemical species and evaluate high-temperature corrosion degrees, along with optimizing operating conditions to prevent high-temperature corrosion. Firstly, a total of 564 Computational Fluid Dynamics (CFD) simulations are performed on a 330 MW tangentially fired boiler, covering various operating conditions, including coal blending, air distribution, boiler load, etc., to obtain a database of O2, CO, and H2S distributions within the boiler. Then a method based on Proper Orthogonal Decomposition (POD) and Support Vector Regression (SVR) is used to process the database to realize real-time prediction of boiler chemical species distribution, which is next utilized as inputs of a high-temperature corrosion evaluation to obtain in-situ corrosion degree distribution. Finally, Particle Swarm Optimization (PSO) is used to optimize coal blending and air distribution schemes, effectively reducing severe corrosion ratio from 36.34 % to 10.04 % in a typical case by improving the atmosphere near the water walls. This study thus provides a new perspective for online boiler diagnostics and digital twin construction, particularly by achieving online monitoring of high-temperature corrosion and optimizing operating conditions to prevent corrosion.

Smoothed Analysis with Adaptive Adversaries

We prove novel algorithmic guarantees for several online problems in the smoothed analysis model. In this model, at each time step an adversary chooses an input distribution with density function bounded above pointwise by \(\tfrac{1}{\sigma }\) times that of the uniform distribution; nature then samples an input from this distribution. Here, σ is a parameter that interpolates between the extremes of worst-case and average case analysis. Crucially, our results hold for adaptive adversaries that can base their choice of input distribution on the decisions of the algorithm and the realizations of the inputs in the previous time steps. An adaptive adversary can nontrivially correlate inputs at different time steps with each other and with the algorithm’s current state; this appears to rule out the standard proof approaches in smoothed analysis. This paper presents a general technique for proving smoothed algorithmic guarantees against adaptive adversaries, in effect reducing the setting of an adaptive adversary to the much simpler case of an oblivious adversary (i.e., an adversary that commits in advance to the entire sequence of input distributions). We apply this technique to prove strong smoothed guarantees for three different problems: (1) Online learning: We consider the online prediction problem, where instances are generated from an adaptive sequence of σ-smooth distributions and the hypothesis class has VC dimension d . We bound the regret by \(\tilde{O}(\sqrt {T d\ln (1/\sigma)} + d\ln (T/\sigma))\) and provide a near-matching lower bound. Our result shows that under smoothed analysis, learnability against adaptive adversaries is characterized by the finiteness of the VC dimension. This is as opposed to the worst-case analysis, where online learnability is characterized by Littlestone dimension (which is infinite even in the extremely restricted case of one-dimensional threshold functions). Our results fully answer an open question of Rakhlin et al. [ 64 ]. (2) Online discrepancy minimization: We consider the setting of the online Komlós problem, where the input is generated from an adaptive sequence of σ-smooth and isotropic distributions on the ℓ 2 unit ball. We bound the ℓ ∞ norm of the discrepancy vector by \(\tilde{O}(\ln ^2(\frac{nT}{\sigma }))\) . This is as opposed to the worst-case analysis, where the tight discrepancy bound is \(\Theta (\sqrt {T/n})\) . We show such \(\mathrm{polylog}(nT/\sigma)\) discrepancy guarantees are not achievable for non-isotropic σ-smooth distributions. (3) Dispersion in online optimization: We consider online optimization with piecewise Lipschitz functions where functions with ℓ discontinuities are chosen by a smoothed adaptive adversary and show that the resulting sequence is \(({\sigma }/{\sqrt {T\ell }}, \tilde{O}(\sqrt {T\ell }))\) -dispersed. That is, every ball of radius \({\sigma }/{\sqrt {T\ell }}\) is split by \(\tilde{O}(\sqrt {T\ell })\) of the partitions made by these functions. This result matches the dispersion parameters of Balcan et al. [ 13 ] for oblivious smooth adversaries, up to logarithmic factors. On the other hand, worst-case sequences are trivially (0, T )-dispersed. 1

The Online Pause and Resume Problem: Optimal Algorithms and An Application to Carbon-Aware Load Shifting

We introduce and study the online pause and resume problem. In this problem, a player attempts to find the k lowest (alternatively, highest) prices in a sequence of fixed length T, which is revealed sequentially. At each time step, the player is presented with a price and decides whether to accept or reject it. The player incurs a switching cost whenever their decision changes in consecutive time steps, i.e., whenever they pause or resume purchasing. This online problem is motivated by the goal of carbon-aware load shifting, where a workload may be paused during periods of high carbon intensity and resumed during periods of low carbon intensity and incurs a cost when saving or restoring its state. It has strong connections to existing problems studied in the literature on online optimization, though it introduces unique technical challenges that prevent the direct application of existing algorithms. Extending prior work on threshold-based algorithms, we introduce double-threshold algorithms for both variants of this problem. We further show that the competitive ratios achieved by these algorithms are the best achievable by any deterministic online algorithm. Finally, we empirically validate our proposed algorithm through case studies on the application of carbon-aware load shifting using real carbon trace data and existing baseline algorithms.